← Clinical Trials
Psoriasis Phase 3 Binary Endpoint NCT01646177

A Study in Participants With Moderate to Severe Psoriasis (UNCOVER-3): Complete Statistical Analysis

This analysis examines the Week 12 response results for ixekizumab, etanercept, and placebo in a randomized trial of participants with moderate to severe plaque psoriasis. It also explains the registry’s analysis methods, uncertainty, sample-size illustrations, secondary outcomes, and safety counts.

Trial start: 2012-07-28  ·  Enrollment: 1346  ·  Sponsor: Eli Lilly and Company
Scope of this record

This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.

1. Trial at a Glance

This page covers the registry results for A Study in Participants With Moderate to Severe Psoriasis (UNCOVER-3) (NCT01646177), a randomized phase 3 study. The primary outcome is Number of Participants Achieving a Static Physician Global Assessment (sPGA) of (0, 1) (Efficacy of Ixekizumab in Participants With Moderate to Severe Chronic Plaque Psoriasis. Measure: sPGA).

1346
Enrollment
Phase 3
4
Arms
In the primary outcome
+34.9 pts
Risk difference
50 mg Etanercept
28.8 to 41.0 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01646177
PhasePhase 3
ConditionPsoriasis
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment1346
Arms in the primary outcome4
Lead sponsorEli Lilly and Company
Results postedYes

2. Clinical Question

Population

The trial enrolled participants with moderate to severe chronic plaque psoriasis. The primary analysis population was all randomized participants. For the non-responder imputation analysis, participants without a Week 12 clinical response or with missing Week 12 data were counted as non-responders.

Intervention

The study compared 80 mg ixekizumab given in two dosing regimens. Dosing Regimen 1 was Q2W through Week 12, and Dosing Regimen 2 was Q4W through Week 12. The registry describes subsequent assignment to a dosing regimen for the long-term extension.

Comparator

The randomized comparison groups were placebo and 50 mg etanercept. The primary endpoint results are reported for placebo, etanercept, and both ixekizumab regimens. The controlled comparison period described in the official title was 12 weeks.

Primary question

At Week 12, how many participants in each group achieved an sPGA score of 0 or 1, meaning clear or minimal psoriasis according to the physician’s assessment? The registry also reports comparisons of each active-treatment group with placebo. The primary endpoint is a binary response: each participant either met the stated response definition or did not.

3. Trial Design

This was a Phase 3, randomized, double-blind, placebo-controlled, parallel-group study. The registry lists quadruple masking. Enrollment was 1346 participants, and the trial is marked completed. The study began on 2012-07-28, with primary completion on 2014-05-22.

The controlled comparison was organized around a 12-week treatment period. Participants were assigned to placebo, 50 mg etanercept, or one of two 80 mg ixekizumab dosing regimens. Regimen 1 used Q2W dosing and Regimen 2 used Q4W dosing during the primary period. The placebo and etanercept arm descriptions also state that participants were assigned to a dosing regimen at Week 12. The official title describes a long-term extension, and the registry includes extension groups with treatment sequences continuing through Week 264 for one ixekizumab regimen.

The primary endpoint was assessed at Week 12. The reported efficacy group sizes were 193 for placebo, 382 for etanercept, 386 for ixekizumab Q4W, and 385 for ixekizumab Q2W. These are the group denominators used in the posted primary outcome results; they do not replace the overall enrollment figure.

The registry identifies psoriasis as the condition and describes the study population as participants with moderate to severe chronic plaque psoriasis. Further details about eligibility criteria, participant characteristics, study sites, randomization procedures, allocation concealment, and the original sample-size justification are not reported in the registry record. The record establishes the randomized, masked, parallel-group structure, but does not give enough detail to reconstruct every operational feature of trial conduct.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Before assignment: This study has 4 periods: Period 1 - Screening; Period 2 - Blinded Induction Dosing Period (Weeks 0 to 12); Period 3 - Long-Term Extension Period (Weeks 12 to 264); Period 4 - Post-Treatment Follow-Up Period (Minimum of 12 Weeks)

Only the first 6 of 12 groups are shown.

Blinded Induction Dosing (Week 0-12)

StagePlacebo50 mg Etanercept (ETN)80 mg Ixekizumab Dosing Regimen 2 (Q4W)80 mg Ixekizumab Dosing Regimen 1 (Q2W)PBO/IXE80Q4WETN/IXE80Q4W
STARTED19338238638500
Received at Least One Dose of Study Drug19338238238400
COMPLETED18336936036300
NOT COMPLETED1013262200

Reasons for not completing this period:

ReasonPlacebo50 mg Etanercept (ETN)80 mg Ixekizumab Dosing Regimen 2 (Q4W)80 mg Ixekizumab Dosing Regimen 1 (Q2W)PBO/IXE80Q4WETN/IXE80Q4W
Adverse Event249800
Protocol Violation138700
Withdrawal by Subject324400
Physician Decision121200
Lack of Efficacy002100
Lost to Follow-up322000

Long-Term Extension Period (Week 12-264)

StagePlacebo50 mg Etanercept (ETN)80 mg Ixekizumab Dosing Regimen 2 (Q4W)80 mg Ixekizumab Dosing Regimen 1 (Q2W)PBO/IXE80Q4WETN/IXE80Q4W
STARTED0000183369
Received at Least One Dose of Study Drug0000183369
COMPLETED0000135256
NOT COMPLETED000048113

Reasons for not completing this period:

ReasonPlacebo50 mg Etanercept (ETN)80 mg Ixekizumab Dosing Regimen 2 (Q4W)80 mg Ixekizumab Dosing Regimen 1 (Q2W)PBO/IXE80Q4WETN/IXE80Q4W
Adverse Event00001634
Withdrawal by Subject00001130
Lost to Follow-up0000617
Lack of Efficacy0000614
Physician Decision000035
Protocol Violation000014
Sponsor Decision000032
Death000013
Clinical Relapse000011
Parent/Caregiver Decision000000
Missing Disposition Form000003

Follow-Up Period (Minimum of 12 Weeks)

StagePlacebo50 mg Etanercept (ETN)80 mg Ixekizumab Dosing Regimen 2 (Q4W)80 mg Ixekizumab Dosing Regimen 1 (Q2W)PBO/IXE80Q4WETN/IXE80Q4W
STARTED000000
Received at Least One Dose of Study Drug000000
COMPLETED000000
NOT COMPLETED000000

Reasons for not completing this period:

ReasonPlacebo50 mg Etanercept (ETN)80 mg Ixekizumab Dosing Regimen 2 (Q4W)80 mg Ixekizumab Dosing Regimen 1 (Q2W)PBO/IXE80Q4WETN/IXE80Q4W
Adverse Event000000
Withdrawal by Subject000000
Lost to Follow-up000000
Lack of Efficacy000000
Protocol Violation000000
Physician Decision000000
Clinical Relapse000000
Sponsor Decision000000
Death000000
Entry Criteria Not Met000000

Analysis population for the primary outcome, as defined in the registry: All randomized participants. Participants who did not meet clinical response criteria or have missing data at Week 12 will be considered non-responders for the Non-Responder Imputation (NRI) analysis.

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

Population: All randomized participants.

CharacteristicUnitPlacebo50 mg Etanercept80 mg Ixekizumab Dosing Regimen 2 (Q4W)80 mg Ixekizumab Dosing Regimen 1 (Q2W)Total
Participants analysed1933823863851346
Age, Categorical: <=18 yearsParticipants00000
Age, Categorical: Between 18 and 65 yearsParticipants1803493583511238
Age, Categorical: >=65 yearsParticipants13332834108
Sex: Female, Male: FemaleParticipants56113128131428
Sex: Female, Male: MaleParticipants137269258254918
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants25525057184
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants133263269259924
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants35676769238
Race (NIH/OMB): American Indian or Alaska NativeParticipants144110
Race (NIH/OMB): AsianParticipants711111241
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants01146
Race (NIH/OMB): Black or African AmericanParticipants8109532
Race (NIH/OMB): WhiteParticipants1763513603611248
Race (NIH/OMB): More than one raceParticipants15129
Race (NIH/OMB): Unknown or Not ReportedParticipants00000
Region of Enrollment: ArgentinaParticipants276621
Region of Enrollment: ChileParticipants1121222276
Region of Enrollment: MexicoParticipants12115
Region of Enrollment: BulgariaParticipants912141348
Region of Enrollment: GermanyParticipants45879090312
Region of Enrollment: HungaryParticipants18313133113
Region of Enrollment: PolandParticipants510111339
Region of Enrollment: RussiaParticipants1122202477
Region of Enrollment: CanadaParticipants22444442152
Region of Enrollment: United StatesParticipants69146147141503

6. Primary Endpoint

The registry lists the primary outcome as Number of Participants Achieving a Static Physician Global Assessment (sPGA) of (0, 1) (Efficacy of Ixekizumab in Participants With Moderate to Severe Chronic Plaque Psoriasis. Measure: sPGA), measured over Week 12.

ElementRegistry entry
Result typeCount Of Participants
Measure of spreadnot applicable
UnitParticipants
Endpoint classificationBinary Endpoint

The primary endpoint counts participants who achieved a static Physician Global Assessment score of 0 or 1 at Week 12. The sPGA is a physician assessment of the overall appearance of psoriasis lesions, based on induration, erythema, and scaling. The scale described in the registry ranges from clear (0) and minimal (1) through mild (2), moderate (3), severe (4), and very severe (5). A response required a post-baseline score of 0 or 1.

This is a binary endpoint: the analysis classifies each participant as a responder or non-responder, rather than measuring the size of each person’s change on a continuous scale. A responder count is direct to interpret, but it does not show how far an individual’s score changed or how close a non-responder came to the response threshold. The primary definition also combines clear and minimal assessments into one response category.

The endpoint is useful for comparing the number of participants meeting a clinically interpretable assessment threshold at a prespecified time. Its meaning depends on the assessment criteria and handling of missing data. In this trial, participants who did not meet response criteria or had missing Week 12 data were considered non-responders in the NRI analysis. The registry does not report additional detail about the assessment process or the original rationale for choosing this endpoint.

7. Results Posted in the Registry

Risk difference: 50 mg Etanercept

+34.9

95% CI: 28.8 to 41.0 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals0.018.436.955.373.792.2Placebo (n=193)50 mg Etanercept (n=382)80 mg Ixekizumab Dosing Regim… (n=386)80 mg Ixekizumab Dosing Regim… (n=385)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)50 mg Etanercept80 mg Ixekizumab Dosing Regim…80 mg Ixekizumab Dosing Regim…-6.331230496785risk difference (percentage points) vs control (95% CI)

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Number of Participants Achieving an sPGA (0) (Efficacy of Ixekizumab in Participants With Moderate to Severe Chronic Plaque Psoriasis. Measure: sPGA)Binary EndpointRisk difference+8.6 pts (5.8 to 11.5)n/a
Number of Participants Achieving ≥90% (PASI 90) Improvement (Efficacy of Ixekizumab in Participants With Moderate to Severe Chronic Plaque Psoriasis. Measure: PASI)Binary EndpointRisk difference+22.5 pts (17.5 to 27.6)37 per arm
Number of Participants Achieving 100% (PASI 100) Improvement (Efficacy of Ixekizumab in Participants With Moderate to Severe Chronic Plaque Psoriasis. Measure: PASI)Binary EndpointRisk difference+7.3 pts (4.7 to 9.9)n/a

Number of Participants Achieving an sPGA (0) (Efficacy of Ixekizumab in Participants With Moderate to Severe Chronic Plaque Psoriasis. Measure: sPGA)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)50 mg Etanercept80 mg Ixekizumab Dosing Regim…-3.266.2016253544risk difference (percentage points) vs control (95% CI)

Number of Participants Achieving ≥90% (PASI 90) Improvement (Efficacy of Ixekizumab in Participants With Moderate to Severe Chronic Plaque Psoriasis. Measure: PASI)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)50 mg Etanercept80 mg Ixekizumab Dosing Regim…-5.401026425773risk difference (percentage points) vs control (95% CI)

Number of Participants Achieving 100% (PASI 100) Improvement (Efficacy of Ixekizumab in Participants With Moderate to Severe Chronic Plaque Psoriasis. Measure: PASI)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)50 mg Etanercept80 mg Ixekizumab Dosing Regim…-3.186.0415243443risk difference (percentage points) vs control (95% CI)

The registry lists secondary measures spanning additional psoriasis response thresholds, physician assessment, itch, quality of life, nail and scalp severity, and body surface area involvement. Across the posted Week 12 responder outcomes, the counts generally follow a pattern in which more participants in the active groups meet the stated response thresholds than in the placebo group. This broad pattern is directionally consistent with the primary sPGA result, but secondary measures capture different aspects of disease and are not interchangeable with the primary endpoint.

Results are posted for 16 secondary measures, while the registry lists 18 outcome measures overall. The record therefore does not contain results for every listed outcome. Secondary results should be interpreted according to the population, time point, endpoint definition, and analysis available for each measure. Some posted comparisons have recalculated unadjusted estimates, while the registry’s own analyses are not reported for every possible group comparison. The displayed outcome summaries should not be treated as a complete account of the planned secondary analysis program.

Unadjusted secondary results carry less inferential weight when many outcomes and comparisons are examined. Each additional test creates another opportunity for a result to appear persuasive by chance, and the record does not report a multiplicity adjustment strategy. A consistent pattern across related outcomes can add context, but it does not erase the risk of selective emphasis or provide the same evidential status as a prespecified primary endpoint. The secondary outcomes are best read as supportive descriptive evidence, with their multiplicity and reporting gaps kept in view.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

9. Statistical Interpretation

Clinical Biostats interpretation

At Week 12, 13 of 193 participants in the placebo group achieved the primary sPGA response. The corresponding counts were 159 of 382 for 50 mg etanercept, 291 of 386 for ixekizumab Q4W, and 310 of 385 for ixekizumab Q2W. The observed response counts were therefore higher in each active-treatment group than in the placebo group. These are descriptive results for the endpoint and time point in the registry; they are not, by themselves, a complete account of treatment effects or of longer-term outcomes.

The recalculated unadjusted risk differences compare each active group’s observed response proportion with the placebo proportion. The estimated differences are positive for all three comparisons, and the reported recalculated confidence intervals are also above zero. The unadjusted p-values are each <0.001. The registry’s own reported Cochran-Mantel-Haenszel analyses also give p <0.001 for each comparison with placebo. These results indicate a clear separation in the posted Week 12 responder data, while the confidence intervals convey uncertainty about the size of that separation.

The observed response counts for the two ixekizumab regimens are both greater than the placebo count and the etanercept count. However, the primary comparisons presented are each against placebo; they do not establish a direct statistical comparison between the ixekizumab regimens or between either ixekizumab regimen and etanercept. A visual or numerical difference between two groups is not a substitute for a reported direct contrast, with its own estimate and uncertainty.

The primary analysis used all randomized participants and treated missing Week 12 outcomes as non-response under NRI. That approach makes the missing-data assumption part of the endpoint result: participants without an observed response are counted as not responding. The registry does not report the amount or pattern of missing data, or sensitivity analyses under alternative missing-data assumptions. Thus, the posted counts should be read with the specified NRI rule in mind, while recognizing that the record does not allow assessment of how alternative missing-data handling might affect the findings.

These findings concern a specific binary measure at Week 12 in this trial. They do not describe every aspect of psoriasis, quality of life, durability, safety, or response beyond the controlled period. Nor do the recalculated unadjusted contrasts replace the sponsor’s own analysis. The registry’s reported analysis is the trial’s stated inferential result; the recalculation is a straightforward comparison of the posted summary counts and is useful as a complementary way to understand the magnitude and precision of the observed group differences.

10. Statistical Methods Explained

What does a responder count represent?

For a binary endpoint, each participant contributes to one of two categories: the response criterion was met, or it was not met. The reported count is the number classified as responders, and the group denominator is the number included in that outcome analysis. The primary outcome uses the Week 12 sPGA definition of a score of 0 or 1. Because the analysis reduces an assessment to a yes-or-no outcome, it is straightforward to compare between groups, but it does not retain all the detail of the underlying clinical scale.

What is a risk difference?

A risk difference compares the response proportions in two groups by subtracting one group’s proportion from the other’s. It is an absolute contrast: it describes how far apart the observed response proportions are, rather than expressing one group as a multiple of the other. A positive risk difference in these comparisons means the active-treatment group had a higher observed response proportion than placebo. The recalculated contrasts are unadjusted comparisons based on posted group counts, not adjusted estimates from the trial’s stratified analysis.

What does a confidence interval add?

A confidence interval gives a range of values compatible with the data under the calculation’s statistical assumptions. It helps readers assess precision: a narrower interval indicates less uncertainty in the estimated contrast, while a wider interval indicates more. The interval is not a guarantee that the true value lies within its limits, and it does not account for every possible source of bias or model error. For the recalculated primary contrasts, the reported intervals lie above zero. That supports the direction of the observed differences under this calculation, but interpretation still depends on the analysis and data assumptions.

How does the registry’s reported test differ?

The registry reports Cochran-Mantel-Haenszel analyses for the comparisons of placebo with etanercept and each ixekizumab regimen. This method can combine evidence across strata when the analysis is organized by strata; the registry does not give further details about the strata or the adjustment. It reports p-values, but does not provide an estimate or confidence interval for those sponsor analyses in the results summarized in the record. A p-value is a measure of how incompatible the observed data are with a specified null hypothesis under the test assumptions. It is not the probability that the null hypothesis is true, nor a measure of clinical importance.

The recalculated p-values are explicitly unadjusted and are based on the posted summary counts. They are not identical in purpose to a stratified sponsor analysis. Where both are available, the sponsor’s reported method is the trial’s own inferential analysis; the simple recalculation offers a transparent unadjusted comparison rather than a replacement for it. The registry record does not state whether other covariates, stratification factors, or additional modeling choices were used in the sponsor analysis.

Why does over-dispersion matter in general?

Over-dispersion is a general concern when variation in data is greater than a statistical model assumes. If a model understates variability, uncertainty intervals may be too narrow and tests may appear more decisive than warranted. The primary outcome is a participant-level binary response, and the registry reports a Cochran-Mantel-Haenszel test rather than a count model. No over-dispersion assessment is reported in the registry record, so it would not be appropriate to claim that it was or was not present. More generally, the relevance of over-dispersion depends on the model and data structure being analyzed.

What analysis details remain unknown?

The record identifies the primary outcome population and the NRI rule, and it lists the reported comparison method. It does not report the complete statistical analysis plan, the original sample-size calculation, a multiplicity procedure, interim analyses, or all implementation details for the sponsor’s analysis. These omissions limit what can be inferred about prespecification and the handling of the full family of outcomes and comparisons. The reported results can still be interpreted on their stated terms, but unreported methods should not be assumed.

11. Confidence Intervals and Precision

The recalculated primary comparisons include confidence intervals for the risk differences between placebo and each active group. Each interval is on the positive side of zero, consistent with the direction of the observed counts. The interval for a contrast communicates uncertainty about its magnitude; it is more informative than a p-value alone because it describes a range of effect sizes compatible with the data under the calculation’s assumptions.

Precision is not the same as certainty about all aspects of the result. The interval reflects sampling variability represented by the unadjusted calculation, but does not capture possible problems such as outcome misclassification, departures from analysis assumptions, missing-data bias, or selective reporting. The registry does not report the confidence interval level for the sponsor’s Cochran-Mantel-Haenszel analyses, and those analyses have p-values but no corresponding estimates or intervals in the record.

The group denominators differ, and the placebo group is smaller than the active groups. That matters when considering how much information contributes to each comparison, although the confidence intervals already express uncertainty according to the recalculation method. The estimates should not be treated as exact descriptions of the underlying response difference. Their interpretation is also limited to the Week 12 primary endpoint and the populations analyzed under the stated NRI rule.

The secondary endpoint results have their own uncertainty and should not inherit the primary endpoint’s precision. For some secondary comparisons, the registry reports counts and recalculated intervals, while its own reported tests are not present for every comparison. A narrow interval or small p-value for one outcome does not resolve multiplicity or missing-data concerns across the broader set of outcomes.

12. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

Effect to detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect2330
75% of the observed effect3647
50% of the observed effect6789
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect205010020040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, pooled-variance normal approximation for two proportions (control proportion held at the observed value). Calculated for the comparison: 50 mg Etanercept.

The sample-size illustrations translate an observed effect into hypothetical planning requirements. For these binary outcomes, the displayed figures are participants per arm, not total participants across both arms and not total events. The calculation assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each scenario asks what sample size would be needed to detect a stated fraction of the observed effect. The trial’s own original design assumptions and sample-size justification are not reported in the registry record.

The 80% power column gives the hypothetical number of participants per arm under the stated assumptions for an 80% chance of detecting the specified effect if that effect were the true one. The 90% power column uses a higher target chance of detection and generally calls for more participants per arm under the same assumptions. These are planning illustrations based on observed results, not evidence that the completed trial had a particular probability of success.

Rows for smaller fractions of the observed effect represent more modest differences to detect. Smaller effects are generally harder to distinguish from random variation, so more participants are needed to achieve the same power target. The curve and rows should therefore be read as sensitivity illustrations: they show how the hypothetical sample requirement changes with the assumed effect size. They do not establish the appropriate sample size for a future study, because that would also require justified assumptions about the target effect, control response, design, and analysis.

This is not observed power. It is a retrospective planning calculation based on the effect seen in the posted data, under the stated assumptions. It does not measure the probability that the trial’s result is true or replace confidence intervals as a way to assess precision.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n = [ z1−α/2 √(2p̄(1−p̄)) + z1−β √(p0(1−p0) + p1(1−p1)) ]2 / (p1 − p0)2

n is the number of participants in each arm, p0 and p1 are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

  1. Control proportion p0 = 0.067; treatment proportion p1 = 0.416; average p̄ = 0.242.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6055 = 1.1868.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.5530 = 0.4654.
  4. n = (1.1868 + 0.4654)2 / (0.3489)2 = 22.4, rounded up to 23 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
p0 <- 0.0673575129533679                          # control proportion
p1 <- 0.416230366492147                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(1646177)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 23 (80% power), 30 (90% power)
 75% of observed effect: n per arm = 36 (80% power), 47 (90% power)
 50% of observed effect: n per arm = 67 (80% power), 89 (90% power)
power.prop.test: 22.4 
Simulated power at n = 23 per arm: 0.846 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

Very small required sample. The formula gives a very small requirement because the observed effect is very large relative to the variability. Normal-approximation formulas are unreliable at such sizes, and the simulation above shows the power actually achieved. An exact or simulation-based design would be needed in practice.

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Cochran-Mantel-Haenszelnot reported< 0.001
Cochran-Mantel-Haenszelnot reported< 0.001
Cochran-Mantel-Haenszelnot reported< 0.001

The registry’s own reported primary analyses use the Cochran-Mantel-Haenszel method for placebo comparisons with etanercept and both ixekizumab regimens. Each reported p-value is <0.001. The registry does not give the corresponding adjusted effect estimates or confidence intervals in these analysis records, so the posted sponsor results establish the reported test results but do not quantify the adjusted contrast in the same way as the recalculation.

The recalculated risk differences use the posted response counts and denominators as simple unadjusted comparisons. They include estimates and confidence intervals, which help describe the size and precision of the crude differences. These calculations answer a related but not identical question to a stratified Cochran-Mantel-Haenszel analysis, and they should not be presented as the trial’s primary analysis.

No discrepancy is flagged between the posted summary statistics and the recalculated results. The sponsor’s own analysis remains the relevant trial analysis, while the recalculation is a supplementary check based on aggregate counts. Neither analysis supports comparisons that were not reported, such as a direct inferential contrast between the two ixekizumab regimens.

15. Multiplicity, Missing Data and Analysis Populations

The study has a primary endpoint, multiple secondary outcomes, and several treatment comparisons. When many hypotheses are tested, the chance of at least one nominally significant finding can increase. Statistical procedures such as family-wise error control or false-discovery control are general ways to address this issue, but the multiplicity strategy for this trial is not reported in the registry record. It is therefore not possible to tell from the record whether the reported tests were adjusted, which outcomes were grouped into testing families, or whether a hierarchy controlled the order of inference.

The primary endpoint population is all randomized participants. The endpoint description states that participants who did not meet response criteria or had missing data at Week 12 were considered non-responders for NRI. This defines how the primary binary response was handled, but the registry does not report the number of missing outcomes, their reasons, or sensitivity analyses using alternative assumptions. NRI is an analysis rule, not proof that missingness has no effect on the estimate.

The record reports the sponsor’s Cochran-Mantel-Haenszel tests, but does not provide the complete statistical analysis plan or details needed to reconstruct all analytic decisions. Interim analyses and stopping rules are not reported in the registry record. The original sample-size justification and its assumptions are also not reported. These gaps make it difficult to evaluate prespecification, the full error-control plan, and whether all planned outcomes were reported.

The listed outcomes exceed the number with posted results. Without further documentation, the absence of results for some measures cannot be interpreted as evidence that the measures were not assessed or that they had a particular result. The posted findings remain interpretable for the reported endpoint and analysis, but broader claims should reflect the incomplete information about multiplicity, missing data, and analysis planning.

16. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Placebo51932.6%
50 mg Etanercept83822.1%
80 mg Ixekizumab Dosing Regimen 2 (Q4W)63821.6%
80 mg Ixekizumab Dosing Regimen 1 (Q2W)93842.3%
PBO/IXE80Q4W Long-Term Extension4518324.6%
ETN/IXE80Q4W Long-Term Extension7136919.2%
IXE80Q4W/IXE80Q4W Long-Term Extension8236022.8%
IXE80Q2W/IXE80Q4W Long-Term Extension5536215.2%
PBO Follow-Up Period51573.2%
ETN Follow-Up Period53091.6%
IXE80Q4W Follow-Up23050.7%
IXE80Q2W Follow-Up63131.9%
Participants with at least one serious adverse event
Serious adverse events by armPlacebo2.6%50 mg Etanercept2.1%80 mg Ixekizumab Dosing Regim…1.6%80 mg Ixekizumab Dosing Regim…2.3%PBO/IXE80Q4W Long-Term Extens…24.6%ETN/IXE80Q4W Long-Term Extens…19.2%IXE80Q4W/IXE80Q4W Long-Term E…22.8%IXE80Q2W/IXE80Q4W Long-Term E…15.2%% of participants with at least one serious adverse event

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

ArmParticipants affected of at risk
Placebo40 of 193
50 mg Etanercept90 of 382
80 mg Ixekizumab Dosing Regimen 2 (Q4W)115 of 382
80 mg Ixekizumab Dosing Regimen 1 (Q2W)123 of 384
PBO/IXE80Q4W Long-Term Extension117 of 183
ETN/IXE80Q4W Long-Term Extension240 of 369

Most frequent serious adverse event terms

Event termOrgan systemPlacebo50 mg Etanercept80 mg Ixekizumab Dosing Regimen 2 (Q4W)80 mg Ixekizumab Dosing Regimen 1 (Q2W)PBO/IXE80Q4W Long-Term ExtensionETN/IXE80Q4W Long-Term Extension
CellulitisInfections and infestations1 of 1930 of 3820 of 3820 of 3843 of 1834 of 369
FallInjury, poisoning and procedural complications1 of 1931 of 3820 of 3821 of 3842 of 1832 of 369
OsteoarthritisMusculoskeletal and connective tissue disorders0 of 1931 of 3820 of 3820 of 3841 of 1834 of 369
Atrial fibrillationCardiac disorders0 of 1930 of 3820 of 3820 of 3842 of 1833 of 369
Myocardial infarctionCardiac disorders0 of 1930 of 3820 of 3820 of 3842 of 1832 of 369
Acute kidney injuryRenal and urinary disorders0 of 1930 of 3821 of 3820 of 3841 of 1832 of 369
Acute myocardial infarctionCardiac disorders1 of 1930 of 3820 of 3820 of 3840 of 1832 of 369
CholelithiasisHepatobiliary disorders0 of 1930 of 3820 of 3821 of 3840 of 1832 of 369
DiverticulitisInfections and infestations0 of 1930 of 3820 of 3820 of 3843 of 1830 of 369
Urinary tract infectionInfections and infestations0 of 1930 of 3820 of 3820 of 3840 of 1833 of 369

Most frequent non-serious adverse event terms

Event termOrgan systemPlacebo50 mg Etanercept80 mg Ixekizumab Dosing Regimen 2 (Q4W)80 mg Ixekizumab Dosing Regimen 1 (Q2W)PBO/IXE80Q4W Long-Term ExtensionETN/IXE80Q4W Long-Term Extension
NasopharyngitisInfections and infestations11 of 19319 of 38229 of 38226 of 38455 of 183104 of 369
Injection site reactionGeneral disorders3 of 19342 of 38243 of 38237 of 38418 of 18324 of 369
HeadacheNervous system disorders5 of 19311 of 38216 of 38216 of 3849 of 18330 of 369
Upper respiratory tract infectionInfections and infestations5 of 1938 of 3828 of 3828 of 38421 of 18333 of 369
ArthralgiaMusculoskeletal and connective tissue disorders4 of 1937 of 3829 of 38213 of 38417 of 18320 of 369
HypertensionVascular disorders2 of 1939 of 3823 of 3825 of 38420 of 18330 of 369
Back painMusculoskeletal and connective tissue disorders2 of 1932 of 3828 of 3827 of 38416 of 18328 of 369
DiarrhoeaGastrointestinal disorders2 of 1936 of 3823 of 38211 of 38410 of 18327 of 369
CoughRespiratory, thoracic and mediastinal disorders0 of 1934 of 3829 of 3826 of 38411 of 18323 of 369
BronchitisInfections and infestations0 of 1934 of 3826 of 3821 of 38417 of 18320 of 369

Serious events with the highest arm-level rate: abortion spontaneous (1.7%), cellulitis (1.6%), diverticulitis (1.6%), cholelithiasis (1.1%), osteoarthritis (1.1%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

For the initial randomized treatment groups, the registry reports serious adverse events in 5 of 193 participants receiving placebo, 8 of 382 receiving etanercept, 6 of 382 in the ixekizumab Q4W safety group, and 9 of 384 in the ixekizumab Q2W safety group. The safety denominators for the ixekizumab groups differ from the efficacy denominators. The counts describe participants with serious adverse events in the registry’s safety summaries; they do not by themselves establish a causal relationship to treatment.

The registry also reports other adverse events, with counts of 40, 90, 115, and 123 in the corresponding initial groups. Longer-term extension and follow-up groups have separate safety counts, but their group sizes and treatment histories differ from those in the initial randomized period. Counts across those groups should not be compared as if they represented equal exposure or a single randomized comparison. Death counts are not reported in the registry record. These summaries provide a limited overview and are not a substitute for event-level descriptions or exposure-adjusted analyses.

17. What the Result Does, and Does Not, Mean

The posted primary results show that more participants in each active-treatment group met the Week 12 sPGA response definition than in the placebo group. The recalculated unadjusted comparisons have positive risk differences with confidence intervals above zero, and the registry reports p < 0.001 for each placebo comparison using its stated analysis method. The data therefore show a substantial separation in the observed Week 12 responder counts within this trial.

This result is specific to the trial population, the treatment regimens, the binary sPGA threshold, and the Week 12 assessment. It does not establish how participants’ scores changed over time, how long responses persisted, or how outcomes differed beyond the controlled period. The study also measured other outcomes, but the primary endpoint alone cannot represent every disease-related or quality-of-life dimension.

The results do not establish a direct statistical difference between the active regimens, because the reported primary comparisons are against placebo. Nor do they resolve safety questions: adverse-event counts are descriptive, and registry summaries alone do not establish causality or provide a full assessment of risk. The longer-term extension data have distinct treatment sequences and group denominators and should not be read as equivalent to the randomized Week 12 comparison.

Statistical significance is not a guarantee that an estimate is unbiased, clinically important, or applicable to every population. Interpretation depends on the trial design, missing-data rule, analysis plan, and the completeness of reporting. Several of those details are not reported in the registry record. The posted results support conclusions about the observed endpoint and stated analyses, but they do not answer every clinical or methodological question about the treatments.

18. Why This Trial Matters Statistically

This trial illustrates how a binary clinical endpoint can make a treatment comparison easy to state while also simplifying the underlying measurement. The sPGA response translates a physician’s graded assessment into a clear-or-minimal threshold. That makes responder counts accessible, but also means the result depends on the chosen cutoff and leaves out distinctions within the non-responder category.

It also shows why effect size and uncertainty should be considered alongside p-values. The registry’s own analyses report small p-values for the placebo comparisons, while the unadjusted recalculations provide risk differences and confidence intervals that describe the direction and precision of the observed contrasts. Those summaries answer related but distinct questions and should not be conflated.

The contrast between the controlled Week 12 period and the long-term extension is statistically important. The randomized comparison is most directly represented by the initial treatment groups and the primary time point. Later treatment sequences and follow-up groups have different histories and denominators, so their counts do not automatically preserve the same comparative interpretation.

Finally, the record demonstrates the limits of registry reporting for methodological review. It identifies the endpoint, population, missing-data rule, reported test, and broad trial structure, while leaving multiplicity procedures, original design assumptions, interim analyses, and several implementation details unreported. Recognizing what is documented and what remains unknown is part of interpreting clinical trial evidence responsibly.

19. Limitations

The primary result is a Week 12 binary response, so it does not describe the full distribution of sPGA scores or the degree of change for participants who did not meet the response threshold. The record does not report an alternate continuous or ordinal analysis of this assessment. Missing outcomes are handled as non-response for the stated NRI analysis, but the amount and pattern of missingness and sensitivity analyses are not reported.

The main inferential comparisons reported are each against placebo. The registry does not provide a direct comparison between ixekizumab dosing regimens or between ixekizumab and etanercept for the primary endpoint. The simple recalculated contrasts are unadjusted and should not be mistaken for such analyses. The sponsor’s reported p-values do not include effect estimates or confidence intervals in the registry records.

Interpretation is also limited by incomplete reporting of the statistical plan. Multiplicity handling, original sample-size justification, interim analyses, and details of the sponsor’s stratified analysis are not reported in the registry record. Results are posted for 16 of the 18 listed outcome measures, so the record does not provide results for every listed measure.

The extension and follow-up safety groups represent different treatment sequences and group sizes, and the record does not provide exposure-adjusted comparisons in these summaries. Serious adverse-event counts alone cannot establish causality or characterize all aspects of safety. The registry describes the target population broadly, but further participant characteristics and eligibility details are not reported in the registry record, limiting assessment of how closely the enrolled participants match other populations.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

Continue through the Clinical Biostats statistical pathway

Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.

23. Record Summary

NCT01646177 is a completed Phase 3 randomized, double-blind, placebo-controlled, parallel-group study of participants with moderate to severe chronic plaque psoriasis. The registry lists enrollment of 1346 and a 12-week controlled comparison of placebo, 50 mg etanercept, and two 80 mg ixekizumab dosing regimens.

The primary endpoint was the number of participants achieving sPGA 0 or 1 at Week 12. Posted response counts were higher in each active group than in placebo. The registry reports Cochran-Mantel-Haenszel p-values of <0.001 for the three comparisons with placebo; unadjusted recalculations also show positive risk differences with confidence intervals above zero.

The record includes secondary outcomes and safety summaries, including a long-term extension, but does not report the multiplicity strategy, original sample-size justification, interim analyses, or all results for the listed outcomes. The findings are specific to the stated endpoint, time point, and analyses.

Clinical Biostats